Anton Shterenlikht

The stress intensity of mixed mode cracks determined by digital image correlation

A generalized approach for determining the stress intensity factors (SIFs) K I and K II for any mode mixity directly from displacement fields obtained by digital image correlation is presented using a centre fatigue cracked aluminium plate as an example problem. It was found that the crack-tip position could be determined on average to within 50 per cent of the displacement vector spacing (60 μm). The approach has been shown to be fairly robust, both in terms of the stability of the SIFs thus obtained and their sensitivity (less than 0.07 MPa

A general method for coupling microstructural response with structural performance

The paper sets out the general principles of a method of coupling finite element for the representation of the structural response with array of cellular automata to encompass the associated microstructural behaviour. For the purpose of this paper, cellular automata is a discrete time–discrete space system consisting of cells which may take one of several states. The state of a cell depends on the states of the neighbouring cells as well as on some macroscopic field variables. The paper goes on to show how these principles can be used, by applying them to problems of oxide scale cracking and of dynamic recrystallization during the hot working of steel, and to the ductile-to-brittle transition in the fracture of ferritic steels.

Three-dimensional cellular automata modelling of cleavage propagation across crystal boundaries in polycrystalline microstructures

A three-dimensional cellular automata (CA) with rectilinear layout is used in this work to create and cleave polycrystalline microstructures. Each crystal is defined by a unique randomly generated orientation tensor. Separate states for grains, grain boundaries, crack flanks and crack fronts are created. Algorithms for progressive cleavage propagation through crystals and across grain boundaries are detailed. The mesh independent cleavage criterion includes the critical cleavage stress and the length scale. Resolution of an arbitrary crystallographic plane within a 26-cell Moore neighbourhood is considered. The model is implemented in Fortran 2008 coarrays. The model gives realistic predictions of grain size and mis-orientation distributions, grain boundary topology and crack geometry. Finally, we show how the proposed CA model can be linked to a finite-element model to produce a multi-scale fracture framework.

Mixed Mode (KI+KII) Stress Intensity Factor Measurement by Electronic Speckle Pattern Interferometry and Image Correlation

The surface displacement fields of a fatigue precracked compact tension sample under tensile load were registered by electronic speckle pattern interferometry and image correlation. The in-plane elastic strain fields calculated from the displacement data were used to obtain the first stress invariant, which for the case of plane stress is proportional to the real part of the first complex potential in Muskhelishvilis approach. Solutions for the stress fields around the crack tip, KI and KII were sought in the form of the Fourier series using Muskhelishvilis complex stress functions. The Fourier series coefficients were calculated from the displacement data using multiple point overdeterministic method (MPODM). The nominal and inferred KI values differ by around 10%; this is probably due in part to mixed mode (KII) loading introduced by some degree of misalignment during the experiment.

Residual stress relaxation measurements across interfaces at macro-and micro-scales using slitting and DIC

In this paper digital image correlation is used to measure relaxation of residual stresses across an interface. On the macro scale the method is applied to a tri-layer bonded aluminium sample, where the middle layer is in tension and the top and the bottom layers are in compression. High contrast speckle pattern was sprayed onto the surface. The relaxation was done with the slitting saw. Three dimensional image correlation was used. On the micro scale the technique was applied to a heat treated large grain brass loaded in tension. Mechanical and electro polishing was used for surface preparation. A focused ion beam was used for slitting across a grain boundary and for imaging. Grain orientation was measured using electron back-scattering diffraction. Two dimensional image correlation was employed. In all macro- and micro-scale experiments the range of measured relaxation was sub-pixel, almost at the limit of the resolution of the image correlation algorithms. In the macro-scale experiments, the limiting factor was low residual stress, due to low shear strength of the Araldite glue used for bonding. Finite element simulation of the relaxation agreed only qualitatively with the experimental results at both size scales. The methodology is intended for use with inverse methods, i.e. the measured relaxation is applied as the boundary conditions to an appropriate FE model which produces stresses equal to the relaxed residual stresses, but with opposite sign. The main conclusion is that the digital image correlation method could be used to measure relaxation caused by slitting in heterogeneous materials and structures at both macro- and micro-scales. However, the repeatability of the techniques needs to be improved before residual stresses can be determined confidently. Acknowledgments The authors gratefully acknowledge Airbus UK for provision of materials. They thank Dr Richard Burguete, Airbus UK, and Prof Peter Flewitt, Department of Physics, University of Bristol, for advice in all aspects of experimental work.

Measuring and predicting the effects of residual stresses on crack propagation

This article presents the first part of a study on the interaction between residual stresses and crack driving force. Blunt notched CT specimens were pre-strained to introduce residual stresses at the notch, where a crack is subsequently introduced. FE modelling is used to model the specimen preload and pre-cracking. Modelling predictions are validated by two different methods. The total predicted surface residual strains are compared to image correlation measurements. The predicted residual strains were measured using neutron diffraction, both before and after fatigue cracking. The residual strain profiles show good agreement with the 3D FE model in the far field but the peak strains measured near the notch are smaller those predicted. This is a result of the low spatial resolution of the technique.

Closed-form solutions of hole distortion for use in deep-hole drilling measurements of residual stress in orthotropic plates

The measurement of residual stress using the deep-hole drilling method relies on the evaluation of the distortion of a hole in a plate under the action of far-field direct and shear stresses. While closed-form solutions exist for the isotropic materials, in previous work for orthotropic materials, finite element analysis has been used to find the distortion. In this technical note, Lekhnitskii’s analysis is used to find closed-form solutions for the distortion of a circular hole in an orthotropic plate. The results are compared with those of finite element analysis for a range of material properties with excellent agreement.

Multi-scale CAFE Framework for Simulating Fracture in Heterogeneous Materials Implemented in Fortran Co-arrays and MPI

Fortran coarrays have been used as an extension to the standard for over 20 years, mostly on Cray systems. Their appeal to users increased substantially when they were standardised in 2010. In this work we show that coarrays offer simple and intuitive data structures for 3D cellular automata (CA) modelling of material microstructures. We show how coarrays can be used together with an MPI finite element (FE) library to create a two-way concurrent hierarchical and scalable multi-scale CAFE deformation and fracture framework. Design of a coarray cellular automata microstructure evolution library CGPACK is described. A highly portable MPI FE library ParaFEM was used in this work. We show that independently CGPACK and ParaFEM programs can scale up well into tens of thousands of cores. Strong scaling of a hybrid ParaFEM/CGPACK MPI/coarray multi-scale framework was measured on an important solid mechanics practical example of a fracture of a steel round bar under tension. That program did not scale beyond 7 thousand cores. Excessive synchronisation might be one contributing factor to relatively poor scaling. Therefore we conclude with a comparative analysis of synchronisation requirements in MPI and coarray programs. Specific challenges of synchronising a coarray library are discussed.

Towards mechanism-based simulation of impact damage using exascale computing

Over the past 60 years, the finite element method has been very successful in modelling deformation in engineering structures. However the method requires the definition of constitutive models that represent the response of the material to applied loads. There are two issues. Firstly, the models are often difficult to define. Secondly, there is often no physical connection between the models and the mechanisms that accommodate deformation. In this paper, we present a potentially disruptive two-level strategy which couples the finite element method at the macroscale with cellular automata at the mesoscale. The cellular automata are used to simulate mechanisms, such as crack propagation. The stress-strain relationship emerges as a continuum mechanics scale interpretation of changes at the micro- and meso-scales. Iterative two-way updating between the cellular automata and finite elements drives the simulation forward as the material undergoes progressive damage at high strain rates. The strategy is particul...

Autotuning of Isotropic Hardening Constitutive Models on Real Steel Buckling Data with Finite Element Based Multistart Global Optimisation on Parallel Computers

An automatic framework for tuning plastic constitutive models is proposed. It is based on multistart global optimisation method, where the objective function is provided by the results of multiple elastoplastic finite element analyses, executed concurrently. Wrapper scripts were developed for fully automatic preprocessing, including model and mesh generation, analysis, and postprocessing. The framework is applied to an isotropic power hardening plasticity using real load/displacement data from multiple steel buckling tests. M. J. D. Powellźs BOBYQA constrained optimisation package was used for local optimisation. It is shown that using the real data presents multiple problems to the optimisation process because (1) the objective function can be discontinuous, yet (2) relatively flat around multiple local minima, with (3) similar values of the objective function for different local minima. As a consequence the estimate of the global minimum is sensitive to the amount of experimental data and experimental noise. The framework includes the verification step, where the estimate of the global minimum is verified on a different geometry and loading. A tensile test was used for verification in this work. The speed of the method critically depends on the ability to effectively parallelise the finite element solver. Three levels of parallelisation were exploited in this work. The ultimate limitation was the availability of the finite element commercial solver license tokens.